your math for the 120W is overrated...you are doing your math based on a 100% efficient PSU. More realistically you are getting 6-8 amps durring opperation. I would still be concerned that it isnt enough power, then you risk burning the spare PSU and possibly the card itself.
Hm. I think I gotta call you out on this one
() The output is measured in volts DC. Just like any PSU. This adapter turns 120v AC into 12v DC.
That is where the inefficiency lies. The power brick is rated at 120W @ 12v. That means it can deliver 120W @ 12v. The inefficiency lies in the AC-->DC conversion, so when the something is drawing 120W DC, the AC adapter is drawing ~134W from the wall (assuming ~90% efficiency) because the AC-->DC conversion is not 100% efficient.
120W @ 12v means 10A. There's no other way to give 120W @ 12v without giving 10A. And one assumption I've made during this post is that the brick can give its full power. Which is a quite safe assumption, as that's what the rating means. That brick can give 10A at 12v maximum.
As for the situation, I say go for it! I think it's totally doable. Under Furmark the 4850 draws ~150W. That means that the PCI-E slot has to give 30W minimum. But in that situation would be out of spec because PCI-E says 75W max per 6pin connector. So to come within spec, the PCI-E slot will have to give its full 75W. That creates a question. What determines where the power comes from? How do we know that the card won't draw 150W from its 6pin connector? Because under Furmark, the card must max out both its PCI-E connection
and its 6pin connector. What's regulating that? Why not just draw 60W from the slot and 90 from the 6pin? IMO, the best option would be to draw ~100W from the 6pin and 50W from the slot.
But also realize that that's furmark. If you deal with a realistic load, the 4850 only peaks at 85W, which is much easier to power. Worst case here is that the slot gives a full 75W, which leaves only 125W for the rest of the system. But that may/may not be an issue depending on the rest of the system. And for every watt under 75 that the PCI-E slot doesn't give will give that much more power dedicated to the system. You could in theory run the 4850 completely on the 12v adapter, assuming you don't run Furmark.
The way I see it, the worst case scenarios are all manageable and safe.